Homework Help:
Behind on Trig Identities

I am currently taking Calc II and we are doing trig substitutions at the moment. I seem to have forgotten almost all the important trig identities. I understand that this sounds like something I should google but I honestly cannot find a good list of the trig identities I should know at this point. If someone could help me with the trig identities that I should memorize I would appreciate it. Thank you.

Edit: An example would be sin(2x)=2sin(x)cos(x) or tan2(x)=sec2(x)-1. Those are two I remember but I know I am forgetting a ton.

I made flashcards, but I agree that you need to practice them with problems. Here are a few of mine:

[itex]
\sin ^2 x + \cos ^2 x = 1
[/itex]

[itex]
\sec ^2 x - \tan ^2 x = 1
[/itex]

[itex]
\csc ^2 x - \cot ^2 x = 1
[/itex]

I don't often run into the half angle identities, but they come up occasionally.

Here's a little trick, so that you don't need to rely on brute memorization. We want to memorize the following well-known identity:

[tex]sin^2 x + cos^2 x = 1[/tex]

If you divide both sides by cos2x, you get:

[tex]tan^2 x + 1 = sec^2 x[/tex]

which is the second identity rearranged. Similarly, if you divide both sides by sin2x, you get:

[tex]1+cot^2 x = csc^2 x[/tex]

which is the third identity rearranged. I can't think of any other identities that can be derived like this, but this saves the effort of memorizing, or provides a sanity check to make sure that what you memorized is correct.